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# Machine Learning - Logistic Regression

## Introduction to Logistic Regression

Logistic regression is a supervised learning classification algorithm used to predict the probability of a target variable. The nature of target or dependent variable is dichotomous, which means there would be only two possible classes.

In simple words, the dependent variable is binary in nature having data coded as either 1 (stands for success/yes) or 0 (stands for failure/no).

Mathematically, a logistic regression model predicts P(Y=1) as a function of X. It is one of the simplest ML algorithms that can be used for various classification problems such as spam detection, Diabetes prediction, cancer detection etc.

## Types of Logistic Regression

Generally, logistic regression means binary logistic regression having binary target variables, but there can be two more categories of target variables that can be predicted by it. Based on those number of categories, Logistic regression can be divided into following types −

### Binary or Binomial

In such a kind of classification, a dependent variable will have only two possible types either 1 and 0. For example, these variables may represent success or failure, yes or no, win or loss etc.

### Multinomial

In such a kind of classification, dependent variable can have 3 or more possible ** unordered** types or the types having no quantitative significance. For example, these variables may represent “Type A” or “Type B” or “Type C”.

### Ordinal

In such a kind of classification, dependent variable can have 3 or more possible ** ordered** types or the types having a quantitative significance. For example, these variables may represent “poor” or “good”, “very good”, “Excellent” and each category can have the scores like 0,1,2,3.

## Logistic Regression Assumptions

Before diving into the implementation of logistic regression, we must be aware of the following assumptions about the same −

In case of binary logistic regression, the target variables must be binary always and the desired outcome is represented by the factor level 1.

There should not be any multi-collinearity in the model, which means the independent variables must be independent of each other.

We must include meaningful variables in our model.

We should choose a large sample size for logistic regression.

## Regression Models

Binary Logistic Regression Model − The simplest form of logistic regression is binary or binomial logistic regression in which the target or dependent variable can have only 2 possible types either 1 or 0.

Multinomial Logistic Regression Model − Another useful form of logistic regression is multinomial logistic regression in which the target or dependent variable can have 3 or more possible

types i.e. the types having no quantitative significance.*unordered*